Question
Download Solution PDFThe displacement of a particle is given by x = (t – 2)2 where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is
Answer (Detailed Solution Below)
Option 2 : 8 m
Detailed Solution
Download Solution PDFConcept:
velocity = distance/ time = dx/dt -----(1)
Calculation:
Given: x = (t – 2)2 where x is in meters and t in seconds
Velocity = 2(t -2) = 2t - 4 ----(2)
Distance traveled = ∫ |v|dt = |t2 - 4t| -----(3)
Here distance traveled can be calculated using equation (2) we get:
At t = 0, v = - 4,
At t = 2, v = 0,
At t = 4, v = 4
= 4t − t2 for t = 0 to 2
= t2 - 4t for t= 2 to 4
The area under the curve shows the distance covered we get:
Distance traveled is = area of Δ OAB + area of Δ BCD
Distance traveled = (4× 2)/2 + (4× 2)/2 = 8m
Hence, option 2) is correct.